Speed, Velocity and Acceleration

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Speed, Velocity and Acceleration

• Linear Motion
• Chapter 2

2
Linear Motion

• Motion is easy to recognize but can be hard to
  describe
• The following quantities are used to describe
  motion speed, velocity and acceleration
• Each of these is a rate. A rate is a quantity
  divided by time.
• Motion along a straight line is sometimes called
  linear motion.

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All Motion is relative

• All motion is relative to a reference.
• This means that we describe motion of an object
  relative to some other object
• In our environment, the reference for motion is
  the earths surface, and speeds are measured
  relative to the earth
• The earth moves at 107,000 km/h relative to the
  sun

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Speed

• Speed is a measure of how fast something is
  moving.
• It is the rate at which a distance is covered
• Units of speed could be km/h, m/s, mi/h, ft/s
• In physics we use units of m/s for speed
• 
  s d/t

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Instantaneous Speed

• Instantaneous speed is speed at any instant in
  time.
• A speedometer measures speed in real time (the
  instantaneous speed).

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Average Speed

• Average speed is the average of all instantaneous
  speeds found simply by a total distance/total
  time ratio
• The average speed of a trip
• For more information http//www.glenbrook.k12.il.u
  s/gbssci/phys/Class/1DKin/U1L1d.html

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Velocity and Speed

• In physics we distinguish between speed and
  velocity
• Speed refers to how quickly an object moves (a
  scalar quantity).
• Velocity is defined as speed in a given direction
  or rate of change of position (displacement over
  time). v x/t
• Velocity refers to both the speed and direction
  of motion of an object (a vector quantity).
• Negative velocity means the object is moving in
  the opposite direction
• Motion at constant velocity means that both the
  speed and direction of an object do not change.
• In a car, we can change the velocity three ways
  gas pedal to speed up, brake to slow down or
  steering wheel to change direction

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Velocity Triangle

• Speed and velocity triangles are similar because
  v x/t
• Find the equation for displacement, and time
  using the triangle
• x v x t
• t x/v

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Velocity Questions

• How far does Bob run if he maintains an average
  velocity of 3 m/s for 10 s?
• List three ways you can change the velocity of
  your car.
• Is it possible to go around a corner without
  changing velocity? Explain.
• One car is going 25 miles/hr north, another car
  is going 25 miles/hr south. Do they have the
  same velocity? Explain.

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Acceleration

• For its velocity to change, an object must
  accelerate.
• An object accelerates whenever its speed or
  direction or both change.
• Acceleration may be positive (increasing speed)
  or negative (decreasing speed).
• Acceleration is a measure of how quickly the
  velocity changes a Dv/t

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Acceleration at constant speed

• An object moving in a circle at constant speed is
  always accelerating (changing direction).

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Solving Acceleration Problems using Acceleration
Triangle

• http//www.glenbrook.k12.il.us/gbssci/phys/mmedia/
  kinema/avd.html
• If you have starting and ending velocity or
  speed, find that before you use the triangle.
• If not, use triangle to find change in velocity
  (Dv), then find initial or final velocity
• Dv ending velocity starting velocity

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More Acceleration Equations

• The equations x v x t and d s x t can only be
  used when the is no acceleration (velocity is
  constant)
• If there is an acceleration and the starting
  velocity is zero, the following equations must be
  used for distance or displacement x ½ at2
  and d ½ at2
• If there is an acceleration, and the starting
  velocity is zero, the following equation
  describes the velocity at any time v a x t or
  v at
• Note If the starting velocity is not zero we use
  the equations v v0 at and x v0t ½
  at2 but student in this class will not be
  required to use these equations

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Acceleration Questions

• A dragster going at 15 m/s increases its velocity
  to 25 m/s in 4 seconds. What is its
  acceleration?
• The driver of a car steps on the brakes, and the
  velocity drops from 20 m/s to 10 m/s in a time of
  2 seconds. Find his acceleration.
• Find the acceleration of a car that travels at a
  constant velocity of 45 Km/hr for 10 s.
• Challenge Calculate the velocity of a
  skateboarder who accelerates from rest for 3
  seconds down a ramp at an acceleration of 5 m/s2.

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Free fall, an example of acceleration

• Free fall is when an object is falling being
  affected only by gravity. That means NO air
  resistance.

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Free Fall All objects fall at the same rate

• If you drop a coin and a feather at the same time
  you will notice that the coin reaches the ground
  way before the feather.
• However, if you were to take the air out of the
  container you would find that the coin and
  feather fall together and hit the bottom at the
  same time!

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Acceleration due to gravity, g

• Newton told us that every object with mass
  attracts every other object with mass and the
  size of the attraction depends on the mass of
  each object and the distance between the objects
• We dont feel the attraction of most objects
  because their mass is small relative to the Earth
  which has a huge mass.
• The Earth pulls so that objects experience an
  acceleration of about 10 m/s2. This acceleration
  is given a special letter, g.
• g 10 m/s2 This number is important, remember
  it!
• So during each second an object is in free fall,
  its velocity increases by 10 m/s. If the object
  experiences air resistance its velocity wont
  increase as fast because air resistance will slow
  it down.

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Challenge Question

• Suppose someone throws a ball straight upward
  with a speed of 30 m/s and at the same time
  throws one straight down with a speed of 30 m/s.
  Which ball will be traveling faster when it hits
  the ground, the one thrown straight upward or the
  one thrown straight down? Assume there is no air
  resistance.

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Time and velocity for an object in free fall

• v gt

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Time and Distance for an object in free fall

• 
  d ½ gt2

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Free Fall Questions How Fast?

• 1) When a ball is thrown straight down, by how
  much does speed increase each second on Earth?
• 2) When a ball is thrown straight up, by how much
  does speed decrease each second?
• 3) In free fall, do a feather and a ball fall
  side by side? Explain.
• 4) An apple falls freely from rest for 8 s on
  Earth, find its speed at 8 s.
• 5) Suppose a rock is dropped on a planet where
  the acceleration due to gravity it 5 m/s2, by how
  much would the speed change each second?
• 6) If a rocket on the planet in 5 falls from
  rest for 3 s, what is its speed at the end of the
  3 s interval?
• 7) Challenge Find g on a planet where a rock has
  a velocity of 120 m/s after 6s of free fall.

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Free Fall Questions How Far?

• For a freely falling rock does the distance
  fallen each second stay the same, increase with
  time, or decrease with time?
• A ball is dropped from rest and freely falls for
  6 s. How many meters has it fallen in 6 s?
• A ball is thrown straight upward and travels 5 m
  until it reaches the top of its path.
• How far will it fall before it reaches its
  initial position?
• How long will it take to fall that distance?
• How long will the ball be in the air?
• 4) A ball is thrown straight up and returns to
  Earth 6 s later.
• Find its speed at the top of its path.
• Find its acceleration at the top its path.
• How long does it take to reach the top of its
  path?
• How fast is it traveling when it returns to
  Earth?
• Challenge What is its maximum height?

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Additional Free Fall Review

• If one had only a stopwatch, could one determine
  the initial speed of a ball launched vertically
  upward from the earths surface? Explain.
• With only a stopwatch, could one determine how
  high the ball travels before it stops? Explain.

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Motion Graphs Position vs. Time
constant, rightward () velocity of 10 m/s
a rightward (), changing velocity - that is, a
car that is moving rightward but speeding up or
accelerating
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Motion Graphs Velocity vs. Time
constant, rightward () velocity of 10 m/s
a rightward (), changing velocity - that is, a
car that is moving rightward but speeding up or
accelerating
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Motion Graph Questions

• 1) What do you think might be happening in this
  graph?

2) What do you think position and velocity graphs
of free fall motion might look like? Try to
sketch them.
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Sources

• http//rigel.physics.unr.edu/faculty/phaneuf/class
  info/index100.html
• Conceptual Physics by Paul Hewitt
• Hs-staffserver.stjames.k12.mn.us/schisa/PowerPoin
  t/Physics/3Chapter2.ppt